I just have a new idea, what I don't like on current chess servers is that you never analyse after the game, so I would suggest a "analysis after the game" option, when enabled you will always get an analysis screen with the board, the opening tree and the engine available after a game. There could also be a "only if my opponent has also analysis after the game enabled, start analysis" or a "start anaysis" button after the game. If both players analyse white gets automatially the control but can give it to the other player. And the markers etc. should be usable of course.

Why am I suggesting those parameters and not only a "start analysis" button like in Fritz? Because when you start an analysis and your opponent doesn't, it's a bit boring. If you can enable an option that you want to analyse, it will become hopefuly more common/popular to analyse after a game.